The Senate is still grappling with how to respond to U.S. military action in Libya, despite new documents from the White House and as their colleagues in the House take an increasingly confrontational stance against President Barack Obama.

On Thursday evening, the No. 2 Democrat Dick Durbin of Illinois unveiled a resolution that would authorize the use of force, short of ground troops, in compliance with the War Powers Act. It would carry the force of law, unlike a resolution crafted by Sens. John Kerry (D-Mass.) and John McCain (R-Ariz.). Two other resolutions are under consideration, as well.

It’s unclear if any will garner a majority of support or if consensus can be reached on bridging the differences, particularly now that dissatisfaction with the White House’s response is palpable.

“They’re doing everything they can to burn goodwill among folks who, generally speaking, have a huge reservoir of good will toward them,” said Sen. Bob Corker (R-Tenn.), a co-sponsor of one of the pending measures on Libya.

“The administration… is trying to have it both ways. I think they’re trying to be involved in this but they don’t want to admit to their base that they’re involved in hostilities,” Corker continued, adding that the White House is saying “one thing in private, and one thing in public” about American engagement in the region.

Corker and Democrat Jim Webb of Virginia wrote a resolution that posed a series of questions to Defense Secretary Robert Gates on the nature of American engagement in Libya. Corker said that he had received classified documents Thursday afternoon from the White House, but that his staff could not review them and he had not yet had a chance to look them over.

But the Tennessee Republican is just one of the many emerging and conflicting voices weighing in on Obama’s decision and plan for Libya.

Foreign Relations Committee Ranking Member Richard Lugar (R-Ind.), who has been an ally of Obama in the past, issued a harsh statement expressing “serious concerns” about the White House’s presentation of the facts Wednesday.

“The administration’s position is both legally dubious and unwise,” Lugar said. “The United States is playing a central and indispensible role in military operations that have no end in sight. The Administration estimates that the cost of these operations will exceed $1 billion by September.”

Meanwhile, McCain stood his ground in support of the military action and vowed to push forward with his resolution.

Earlier this week, McCain suggested he had strengthened his language with Kerry, including increased reporting requirements for the White House to track progress in the region.

And it’s not just Republicans torn on the issue. If Democrats were united, Kerry would have brought up his resolution in committee. His office said they postponed the meeting to give senators time to review the documents released Wednesday by the White House, but some aides suggested the unclassified report were short enough to get through in time.

Durbin had been in discussions with Kerry for more than a week, hoping to get authorizing language into the Kerry-McCain offering either before the panel convened, during the mark-up or once the resolution got to the floor. Durbin’s joint resolution with Sen. Ben Cardin (D-Md.) announced Thursday could put pressure on the two key members to include such language in whatever agreement they bring before the committee.

To make matters worse for the Senate, the administration and the House continue to dig in on the matter, drawing more intractable lines and edging the uncertain upper chamber out of the debate.

Speaker John Boehner (R-Ohio) threatened to cut funding from the mission Thursday if he and his members were unsatisfied with information they were getting from the White House.

White House spokesman Jay Carney later bristled at a series of questions on Libya, saying, “I don’t anticipate further elucidation of our reasoning, because I think it was quite clear.”

Defunding the Libyan engagement, however, no matter how unpopular the mission is with senators, is an approach unlikely to be embraced by the traditionally more measured upper chamber.

“I don’t see anything wrong with that, everybody knows that Congress has the power of the purse, is that a revelation?” McCain said. “I don’t second-guess what Rep. Boehner has to say — he obviously has a very unhappy conference.”